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Simplifying 18x2 + 25x + 3 = 0 Reorder the terms: 3 + 25x + 18x2 = 0 Solving 3 + 25x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.1666666667 + 1.388888889x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 1.388888889x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 1.388888889x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 1.388888889x + x2 = 0 + -0.1666666667 1.388888889x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 1.388888889x + x2 = -0.1666666667 The x term is 1.388888889x. Take half its coefficient (0.6944444445). Square it (0.4822530865) and add it to both sides. Add '0.4822530865' to each side of the equation. 1.388888889x + 0.4822530865 + x2 = -0.1666666667 + 0.4822530865 Reorder the terms: 0.4822530865 + 1.388888889x + x2 = -0.1666666667 + 0.4822530865 Combine like terms: -0.1666666667 + 0.4822530865 = 0.3155864198 0.4822530865 + 1.388888889x + x2 = 0.3155864198 Factor a perfect square on the left side: (x + 0.6944444445)(x + 0.6944444445) = 0.3155864198 Calculate the square root of the right side: 0.561770789 Break this problem into two subproblems by setting (x + 0.6944444445) equal to 0.561770789 and -0.561770789.Subproblem 1
x + 0.6944444445 = 0.561770789 Simplifying x + 0.6944444445 = 0.561770789 Reorder the terms: 0.6944444445 + x = 0.561770789 Solving 0.6944444445 + x = 0.561770789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6944444445' to each side of the equation. 0.6944444445 + -0.6944444445 + x = 0.561770789 + -0.6944444445 Combine like terms: 0.6944444445 + -0.6944444445 = 0.0000000000 0.0000000000 + x = 0.561770789 + -0.6944444445 x = 0.561770789 + -0.6944444445 Combine like terms: 0.561770789 + -0.6944444445 = -0.1326736555 x = -0.1326736555 Simplifying x = -0.1326736555Subproblem 2
x + 0.6944444445 = -0.561770789 Simplifying x + 0.6944444445 = -0.561770789 Reorder the terms: 0.6944444445 + x = -0.561770789 Solving 0.6944444445 + x = -0.561770789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6944444445' to each side of the equation. 0.6944444445 + -0.6944444445 + x = -0.561770789 + -0.6944444445 Combine like terms: 0.6944444445 + -0.6944444445 = 0.0000000000 0.0000000000 + x = -0.561770789 + -0.6944444445 x = -0.561770789 + -0.6944444445 Combine like terms: -0.561770789 + -0.6944444445 = -1.2562152335 x = -1.2562152335 Simplifying x = -1.2562152335Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1326736555, -1.2562152335}
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